Torsion group Z/2Z × Z/4Z, rank = 9


Dujella - Peral (2012)

y2 = x3 + x2 - 6141005737705911671519806644217969840x 
    + 5857433177348803158586285785929631477808095171159063188

	Torsion points:

O, [-2861469472720778854, 0], 
[1431017969855150171, 0], 
[1430451502865628682, 0], 
[1381707195787460036, -100990010591667129753450630], 
[1381707195787460036, 100990010591667129753450630], 
[1480328743922840306, -103337259355706972940063720], 
[1480328743922840306, 103337259355706972940063720]

	Independent points of infinite order:

P1 = [-612695149795875652, 3064309824349077381027308358] 
P2 = [-431590874944672564, 2903005768083873104158859430]
P3 = [187501554154394546, 2170847073897415394832351000]
P4 = [-1383500708967173302, 3421314943163833774567917408]
P5 = [1428519047239049546, 4551549120021779137548000]
P6 = [1430248713837731282, 818226000869154831593640]
P7 = [1429305792931194266, 2901212522992755483557760]
P8 = [103900694057898826, 2284841365124562079087206240]
P9 = [1429854291102331316, 1726936504767203175719910]

Some curves with torsion group Z/2Z × Z/4Z and rank = 6, 7 or 8
High rank curves with prescribed torsion Andrej Dujella home page